That would put it in line with Pandora's public valuation, and ahead of other recent entrants into the billion-dollar club on AirBnb and Spotify.

The company has been showing some pretty spectacular growth lately -- for instance, in April it was processing $2 million a day, and now it's above $3 million.

But existing payment processors like Verifone aren't about to roll over, and the company faces challenges from tech giants like Google, which is pushing its NFC-based mobile payment system, Wallet.

The report says that investors are mixed whether Square is worth $2 billion or not.

We're hearing that a lot about startup valuations these days -- without a look at the books and some confident predictions of future cash flow, nobody has any idea what Square or any other startup is worth. Place your bets.